Controller reduction by component cost analysis

q-Markov covariance equivalent realizations

“…to give the form (2.12). An algorithm is given in the Appendix ofYousuffand Skelton (1984). This form is slightly less restrictive than block Hessenberg (since rows of zeros are assigned after the blocks Ai,i+ 1 only up to i = q -I.…”

“…This form is slightly less restrictive than block Hessenberg (since rows of zeros are assigned after the blocks Ai,i+ 1 only up to i = q -I. However, we simply stop the block Hessenberg construction of Yousuff and Skelton (1984) …”

“…Find all I-Markov COVERs of Finally, in this section we must show how the class of q-Markov COVERs defined in this paper relates to the specific q-Markov COVER derived earlier by Yousuff et al (1985).…”

“…It is proven in Yousuff et al (1985) that (3.17) is related by a similarity transformation P to a truncation of the cost decoupled coordinates (2.12). A truncation of (2.12) is equivalent to ( R=GJp-{p-'[I o{~Jp-*J'=GJp which is precisely the projection (2.2) used to develop the results of § 4 if G = 0 and T = I (since we started with coordinates (2.12)).…”

“…If the realization (A 2, D 2, C 2) has these two properties: An algorithm is available (Yousuff et al 1985) which constructs a q-Markov COVER for any finite q and this algorithm has been applied to the controller reduction problem ofYousuffand Skelton (1984). This procedure generates a specific member of a broader class of q-Markov COVERs which are described in this paper.…”